Basic properties
| Modulus: | \(8670\) | |
| Conductor: | \(4335\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(68\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4335}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8670.bs
\(\chi_{8670}(47,\cdot)\) \(\chi_{8670}(293,\cdot)\) \(\chi_{8670}(557,\cdot)\) \(\chi_{8670}(803,\cdot)\) \(\chi_{8670}(1067,\cdot)\) \(\chi_{8670}(1313,\cdot)\) \(\chi_{8670}(1577,\cdot)\) \(\chi_{8670}(1823,\cdot)\) \(\chi_{8670}(2087,\cdot)\) \(\chi_{8670}(2333,\cdot)\) \(\chi_{8670}(2597,\cdot)\) \(\chi_{8670}(2843,\cdot)\) \(\chi_{8670}(3107,\cdot)\) \(\chi_{8670}(3353,\cdot)\) \(\chi_{8670}(3617,\cdot)\) \(\chi_{8670}(3863,\cdot)\) \(\chi_{8670}(4127,\cdot)\) \(\chi_{8670}(4637,\cdot)\) \(\chi_{8670}(4883,\cdot)\) \(\chi_{8670}(5147,\cdot)\) \(\chi_{8670}(5393,\cdot)\) \(\chi_{8670}(5657,\cdot)\) \(\chi_{8670}(5903,\cdot)\) \(\chi_{8670}(6167,\cdot)\) \(\chi_{8670}(6413,\cdot)\) \(\chi_{8670}(6677,\cdot)\) \(\chi_{8670}(6923,\cdot)\) \(\chi_{8670}(7433,\cdot)\) \(\chi_{8670}(7697,\cdot)\) \(\chi_{8670}(7943,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{68})$ |
| Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((2891,6937,6361)\) → \((-1,i,e\left(\frac{25}{68}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8670 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{65}{68}\right)\) | \(e\left(\frac{55}{68}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{65}{68}\right)\) | \(e\left(\frac{21}{68}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{25}{68}\right)\) | \(e\left(\frac{57}{68}\right)\) |